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Complex dynamics in a singular Leslie–Gower predator–prey bioeconomic model with time delay and stochastic fluctuations

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  • Zhang, Yue
  • Zhang, Qingling
  • Yan, Xing-Gang

Abstract

In this paper, a class of singular Leslie–Gower predator–prey bioeconomic models with environment fluctuations and time delays is investigated. Local stability analysis of the model reveals that there is a phenomenon of singularity induced bifurcation due to variation of economic interest of harvesting. By choosing the delay as a bifurcation parameter, it is shown that the Hopf bifurcations can occur as the delay crosses some critical values. Then, the effect of a fluctuating environment on the singular stochastic delayed predator–prey bioeconomic model is discussed. Finally numerical simulations demonstrate that the amplitude of oscillation for population is enhanced when compared with the oscillation observed in the deterministic environment.

Suggested Citation

  • Zhang, Yue & Zhang, Qingling & Yan, Xing-Gang, 2014. "Complex dynamics in a singular Leslie–Gower predator–prey bioeconomic model with time delay and stochastic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 180-191.
    • Handle: RePEc:eee:phsmap:v:404:y:2014:i:c:p:180-191
    DOI: 10.1016/j.physa.2014.02.013
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    References listed on IDEAS

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    1. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
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    3. Lin Wang & Xiang Li & Yi-Qing Zhang & Yan Zhang & Kan Zhang, 2011. "Evolution of Scaling Emergence in Large-Scale Spatial Epidemic Spreading," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-11, July.
    4. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
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    Cited by:

    1. Liu, Chao & Wang, Luping & Zhang, Qingling & Yan, Yun, 2017. "Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 682-698.
    2. Wang, Xingyuan & Zhao, Tianfang & Qin, Xiaomeng, 2016. "Model of epidemic control based on quarantine and message delivery," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 168-178.
    3. Liu, Chao & Wang, Luping & Zhang, Qingling & Li, Yuanke, 2018. "Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1216-1239.
    4. Liu, Chao & Xun, Xinying & Zhang, Qingling & Li, Yuanke, 2019. "Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 99-118.
    5. Nosrati, Komeil & Shafiee, Masoud, 2017. "Dynamic analysis of fractional-order singular Holling type-II predator–prey system," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 159-179.
    6. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Liu, Chao & Yu, Longfei & Zhang, Qingling & Li, Yuanke, 2018. "Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 115-137.

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